Existence and Calculation of Optimal Equilibria on Overlapping Generations Economies

Leandro Lyra Braga Dognini

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Abstract: A well-known feature of overlapping generations economies is that the First Welfare Theorem fails and equilibrium may be inefficient. The Cass (1972) criterion furnishes a necessary and sufficient condition for efficiency, but does not address the matter of existence of efficient equilibria, and Cass, Okuno, and Zilcha (1979) provide nonexistence examples. I develop an algorithm based on successive approximations of a nonstationary, consumption-loan, prone to savings, overlapping generations economy with finite-lived heterogeneous agents to find elements of its set of equilibria as the limit of nested compact sets. These compact sets are the result of a backward calculation through equilibrium equations that departs from the set of Pareto optimal equilibria of well-behaved tail economies. The equilibria calculated through this algorithm satisfy the Cass (1972) criterion and are used to derive the existence results on efficient equilibria.

Date: 2025-09
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